Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile.
Phys Rev E. 2018 Jan;97(1-1):012907. doi: 10.1103/PhysRevE.97.012907.
The critical phenomena associated to the liquid-to-solid transition of quasi-two-dimensional vibrated granular systems is studied using molecular dynamics simulations of the inelastic hard sphere model. The critical properties are associated to the fourfold bond-orientational order parameter χ_{4}, which measures the level of square crystallization of the system. Previous experimental results have shown that the transition of χ_{4}, when varying the vibration amplitude, can be either discontinuous or continuous, for two different values of the height of the box. Exploring the amplitude-height phase space, a transition line is found, which can be either discontinuous or continuous, merging at a tricritical point and the continuous branch ends in an upper critical point. In the continuous transition branch, the critical properties are studied. The exponent associated to the amplitude of the order parameter is β=1/2, for various system sizes, in complete agreement with the experimental results. However, the fluctuations of χ_{4} do not show any critical behavior, probably due to crossover effects by the close presence of the tricritical point. Finally, in quasi-one-dimensional systems, the transition is only discontinuous, limited by one critical point, indicating that two is the lower dimension for having a tricritical point.
使用非弹性硬球模型的分子动力学模拟研究了准二维振动颗粒系统的液-固转变相关的临界现象。临界性质与四重键取向序参数 χ_{4}相关联，它衡量系统的方形结晶度水平。先前的实验结果表明，当改变振动幅度时，对于盒高的两个不同值，χ_{4}的转变可以是不连续的或连续的。在振幅-高度相空间中，发现了一条转变线，它可以是不连续的或连续的，在三叉点处合并，连续分支在一个上临界点处结束。在连续转变分支中，研究了临界性质。对于各种系统尺寸，参数振幅的指数 β=1/2，与实验结果完全一致。然而，χ_{4}的涨落没有显示出任何临界行为，可能是由于三叉点的近距离存在导致了交叉效应。最后，在准一维系统中，转变仅为不连续，受一个临界点限制，表明二维是存在三叉点的下限维度。
